Solve the following differential equations: $\frac{{\mathrm{d}}^{2}y}{\mathrm{d}x^{2}}=2$ where \(

Question

Solve the following differential equations: $\frac{{\mathrm{d}}^{2}y}{\mathrm{d}x^{2}}=2$ where $x=0$, $\frac{\mathrm{d}y}{\mathrm{d}x}=2$, $y=4$ $\sec^{2}x\frac{{\mathrm{d}}^{2}y}{\mathrm{d}x^{2}}+2=0$ $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{1}{x\ln x}$

Accepted Answer

$\text{(i)}\ y=x^2+2x+4$ $\text{(ii)}\ y=\frac{1}{4}\cos2x-\frac{x^2}{2}+C_1x+C_2,\ \cos x\ne0$ $\text{(iii)}\ y=\ln|\ln x|+C,\ x>0,\ x\ne1$

Differential Equations - Second-Order Linear Differential Equations

Differential Equations - Second-Order Linear Differential Equations

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